| Title: |
Anisotropic spaces for the bilateral shift |
| Authors: |
Marra, Mateus, Smania, Daniel |
| Publication Year: |
2024 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Dynamical Systems, Mathematics - Analysis of PDEs, Mathematics - Functional Analysis, 37A25, 37A30, 37A46, 37C30, 37D05, 37D35, 37D20, 43A85, 47B37, 43A15, 46E36, 46F99 |
| More Details: |
Given two H\"older potentials $\phi_+$ and $\psi_-$ for the unilateral shift, we define anisotropic Banach spaces of distributions on the bilateral shift space with a finite alphabet. On these spaces, the transfer operator for the bilateral shift is quasicompact with a spectral gap, and the unique Gibbs state associated with $\phi_+$ spans its $1$-eigenspace. This result allows us to establish exponential decay of correlations for H\"older observables and a wide range of measures on the bilateral shift space.
Comment: 34 pages, 1 figure |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2411.15050 |
| Accession Number: |
edsarx.2411.15050 |
| Database: |
arXiv |
